The pattern of the ones-digits is 9, 8, 7, 6, 5, 4, 3, 2, 1, 0. This pattern is repeated for the next ten multiples, over and over.

5. A power of nine is a multiple of nine by itself. The first power of nine is 9. The second power of 9 is 9×9. The third power of nine is 9x9x9. The ones-digits of powers of nine form a pattern. What is the pattern?

The first power of 9 is 9. The second power is 81. The third power is 729. Multiplying 729 by 9 would have a ones-digit of 1. The next power of 9 would then have a ones-digit of 9.

The pattern is 9, 1, 9, 1, 9, 1 and so on. Alternating 9s and 1s.

Bonus question: of the numbers from 1 through 8, what are the patterns of ones-digits of their powers?

Week 2: Multiplication – Day 3

1. What are the factors of 9?

The factors of 9 are 1, 9, and 3.

2. Is 3 a factor of 21?

Yes, 3 is a factor of 21 because 3 x 7 = 21.

3. Is 6 a factor of 33?

No. 33 is in between two multiples of 6. 33 divided by 6 is 5 with remainder 3. 6 x 5 = 30 and 6 x 6 = 36, and 33 is between.

4. What are all of the factors of 42?

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.

In pairs: 1 and 42; 2 and 21; 3 and 14; 6 and 7.

5. Every counting number has at least two factors. What are these two factors?

(A counting number is a positive whole number, such as 1, 2, 3, 4, 5, 6, and so on.) For example, what are the two factors of 7?

1 is a factor of every number. And every number is a factor of itself.

The two factors of 7 are 1 and 7.

Week 2: Multiplication – Day 2

Notice that adding and multiplying look quite different! Draw some more pictures of adding vs. multiplying.